Equivariant algebraic vector bundles over representations of reductive groups: theory.
Clicks: 243
ID: 97349
1991
Let G be a reductive algebraic group and let B be an affine variety with an algebraic action of G. Everything is defined over the field C of complex numbers. Consider the trivial G-vector bundle B x S = S over B where S is a G-module. From the endomorphism ring R of the G-vector bundle S a construction of G-vector bundles over B is given. The bundles constructed this way have the property that when added to S they are isomorphic to F + S for a fixed G-module F. For such a bundle E an invariant rho(E) is defined that lies in a quotient of R. This invariant allows us to distinguish nonisomorphic G-vector bundles. This is applied to the case where B is a G-module and, in that case, an invariant of the underlying equivariant variety is given too. These constructions and invariants are used to produce families of inequivalent G-vector bundles over G-modules and families of inequivalent G actions on affine spaces for some finite and some connected semisimple groups.
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masuda1991equivariantproceedings
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| Authors | Masuda, M;Petrie, T; |
| Journal | Proceedings of the National Academy of Sciences of the United States of America |
| Year | 1991 |
| DOI | DOI not found |
| URL | URL not found |
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